PhaseFlow4D: Physically Constrained 4D Beam Reconstruction via Feedback-Guided Latent Diffusion

• URL: http://arxiv.org/abs/2604.03885v2
• Date: Tue, 07 Apr 2026 16:43:31 GMT
• Title: PhaseFlow4D: Physically Constrained 4D Beam Reconstruction via Feedback-Guided Latent Diffusion
• Abstract summary: PhaseFlow4D reconstructs and tracks the full 4D phase space from incomplete 2D observations alone.<n>We validate on multi-particle simulations of heavy-ion beams at the Facility for Rare Isotope Beams.
• Score: 78.29352305480285
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We address the problem of recovering a time-varying 4D distribution from a sparse sequence of 2D projections - analogous to novel-view synthesis from sparse cameras, but applied to the 4D transverse phase space density $ρ(x,p_x,y,p_y)$ of charged particle beams. Direct single shot measurement of this high-dimensional distribution is physically impossible in real particle accelerator systems; only limited 1D or 2D projections are accessible. We propose PhaseFlow4D, a feedback-guided latent diffusion model that reconstructs and tracks the full 4D phase space from incomplete 2D observations alone, with built-in hard physics constraints. Our core technical contribution is a 4D VAE whose decoder generates the full 4D phase space tensor, from which 2D projections are analytically computed and compared against 2D beam measurements. This projection-consistency constraint guarantees physical correctness by construction - not as a soft penalty, but as an architectural prior. An adaptive feedback loop then continuously tunes the conditioning vector of the latent diffusion model to track time-varying distributions online without retraining. We validate on multi-particle simulations of heavy-ion beams at the Facility for Rare Isotope Beams (FRIB), where full physics simulations require $\sim$6 hours on a 100-core HPC system. PhaseFlow4D achieves accurate 4D reconstructions 11000$\times$ faster while faithfully tracking distribution shifts under time-varying source conditions - demonstrating that principled generative reconstruction under incomplete observations transfers robustly beyond visual domains.

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